Field of Invention
The present invention relates to a technical field of materials microstructure characterization and crystal structure analysis, and more particularly to a method for determining a primitive reciprocal basis of unknown crystals based on single EBSD pattern.
Description of Related Arts
Electron backscatter diffraction (EBSD) is an important complement to scanning electron microscope (SEM), which has been widely used in crystal orientation analysis of materials in the past 20 years. With this technique, EBSD pattern of crystalline samples is collected on the SEM. An EBSD pattern provides a variety of crystallographic information. Usually, an EBSD pattern comprises dozens of Kikuchi bands. The Kikuchi band width is related to interplanar spacing of a characterized crystal. The Length and direction of reciprocal vectors of the crystal are able to be identified according to the width and azimuth of the Kikuchi bands. The Kikuchi bands intersect each other to form Kikuchi poles, wherein each Kikuchi pole is equivalent to a 2D reciprocal plane. An EBSD pattern generally comprises over a hundred of Kikuchi poles, which are equivalent to over a hundred of 2D reciprocal planes of the crystal. The above diffraction information is applicable to analysis of unknown crystal Bravais lattices (reference: L. L. Li and M. Han. Determining the Bravais lattice using a single electron backscatter diffraction pattern. J. Appl. Cryst. 48(2015):107-115).
The conventional methods for determining unknown crystal lattices are mainly X-ray diffraction (XRD) and selected-area electron diffraction (SAED). These classic methods have their own advantages and disadvantages. For the former one, analysis of cell parameters is highly accurate, and atomic coordinates inside the cell is able to be further accurately positioned according to diffraction intensity. However, microstructure morphology of the sample is not able to be real-time observed, and the sample is usually required to be a single phase. For the latter one, users are allowed to real-time observe the microstructure of the sample through a transmission electron microscope, and electron diffraction is provided to interested areas, so as to analyze crystallographic information while observe microstructure morphology, wherein that is the biggest advantage of SAED. The disadvantage of the latter is that the sample is difficult to prepare. The EBSD technique allows the users to directly characterize the microstructure morphology of the materials through the SEM, which keeps the advantage of the SAED. More importantly, because of using the SEM, sample preparation is greatly simplified. Determining 3D primitive reciprocal basis based on single EBSD pattern is conducive to reconstructing unknown lattice of bulk crystals, which is a novel application of EBSD technique.
Conventionally, the applicant disclosed analysis of Bravais lattice of unknown crystals based on EBSD patterns in references comprising: 3D reconstruction for Bravais lattice of unknown crystals using EBSD pattern. Journal of Chinese Electron Microscopy Society, December 2008, Vol. 27, No. 6; 3D reconstruction for Bravais lattice of hexagonal crystal using single EBSD pattern. Journal of Chinese Electron Microscopy Society, Aug. 2010, Vol. 29, No. 4; Reconstruction for 3D primitive reciprocal cell of crystals using EBSD pattern. Paper collection of the second National Symposium on electron backscatter diffraction (EBSD) technology and application, the Sixth National Symposium on science and technology, Dec. 31, 2007; and Chinese patent application No. 200810237624.X, Method for determining unknown crystal Bravais lattice using electron backscatter diffraction.
According to the above references, the applicant is the first to disclose geometrically determining Bravais lattices of unknown crystals based on single EBSD pattern, which means using a large amount of 2D reciprocal plane information, 3D reconstruction for reciprocal lattice, and reciprocal-direct space transformation. During reconstruction of Bravais lattice of unknown crystals, selection of a set of 3D primitive basis is a key point. For 3D lattice reconstruction, cell selection is not unique, which may comprise primitive cell and non-primitive cell. The primitive cells are only of one lattice point. Theoretically, all primitive cells for a given crystal have the same volume, moreover, primitive cell is always of the smallest volume in all cells, and the volume of the non-primitive cells should be integral multiple of the smallest one. However, because edge contrast of the Kikuchi bands in EBSD patterns is usually ambiguous, the measured error of the Kikuchi band width is large, which is up to 20% (reference: D. J. Dingley and S. I. Wright. Determination of crystal phase from an electron backscatter diffraction pattern. J. Appl. Cryst. 42(2009):234-241). In this case, cell volumes appear to continuously change. More critically, because of the deviation of the Kikuchi band trace line, fake cell volumes usually occur. Correct identification of a 3D primitive basis is a premise of determining Bravais lattice of unknown crystals. The present invention takes full advantage of the characteristic that there is a variety of crystallographic information in single EBSD pattern, and provides a method for correctly selecting a 3D primitive reciprocal basis from a single EBSD pattern.
For shortcomings of the conventional technique, the present invention is provided.